The Variable Stiffness Treadmill 2: Development and Validation of a Unique Tool to Investigate Locomotion on Compliant Terrains

Abstract

Understanding legged locomotion in various environments is valuable for many fields, including robotics, biomechanics, rehabilitation, and motor control. Specifically, investigating legged locomotion in compliant terrains has recently been gaining interest for the robust control of legged robots over natural environments. At the same time, the importance of ground compliance has also been highlighted in poststroke gait rehabilitation. Currently, there are not many ways to investigate walking surfaces of varying stiffness. This article introduces the variable stiffness treadmill (VST) 2, an improvement of the first version of the VST, which was the first treadmill able to vary belt stiffness. In contrast to the VST 1, the device presented in this paper (VST 2) can reduce the stiffness of both belts independently, by generating vertical deflection instead of angular, while increasing the walking surface area from 0.20 m² to 0.74 m². In addition, both treadmill belts are now driven independently, while high-spatial-resolution force sensors under each belt allow for measurement of ground reaction forces and center of pressure. Through validation experiments, the VST 2 displays high accuracy and precision. The VST 2 has a stiffness range of 13 kN/m to 1.5MN/m, error of less than 1%, and standard deviations of less than 2.2 kN/m, demonstrating its ability to simulate low-stiffness environments reliably. The VST 2 constitutes a drastic improvement of the VST platform, a one-of-its-kind system that can improve our understanding of human and robotic gait while creating new avenues of research on biped locomotion, athletic training, and rehabilitation of gait after injury or disease.

Keywords: biped locomotion; gait; mechanisms and robots; rehabilitation; variable stiffness.

Fig. 1

The VST 2 with a subject walking on it while wearing a harness-based body weight support. The subject is equipped with 22 motion capture markers as well as 10 EMG electrodes tracking muscle activity. The left figure shows the right belt at a lower stiffness than the left, resulting in a vertical deflection. The right figure shows the opposite.

Fig. 2

The VST 2 with the right treadmill platform removed to expose inner mechanisms

Fig. 3

Simplified kinematics of VST 2, where (a) shows the actual spring positioning and (b) shows an equivalent resting spring that will be used for the kinematic derivation

Fig. 4

The variable stiffness mechanism at an arbitrarily low stiffness, resulting in a deflection when force is applied

Fig. 5

One VST 2 platform with force mats installed

Fig. 6

Block diagrams for (a) the variable stiffness mechanism and (b) the treadmill belts

Fig. 7

Experimental stiffness values tested with 70 kg at six different values of the carriage position and compared to theoretical stiffness curve. Blue and orange points denote the average experimental and theoretical stiffness values, respectively, while black error bars indicate variations of one standard deviation across trials. The blue dashed line represents the best-fit curve of the experimental data.

Fig. 8

Step responses with a 70 kg static mass at stiffness levels of 18, 21, 26, 33, 45, and 63 kN/m. Solid and dashed lines denote the actual and desired treadmill vertical displacement for each stiffness level, respectively.

Fig. 9

Deflection of the platform over a single gait cycle at multiple stiffness levels with a 90 kg subject. A position of 0 mm corresponds to the unloaded, rigid platform. Note: The low-stiffness perturbations were unilateral. 0% at the gait cycle denotes the heel-strike event.

Fig. 10

Force applied on a single platform over a gait cycle at multiple stiffness levels with a 90 kg subject. 0% at the gait cycle denotes the heel-strike event.

Fig. 11

Center of pressure path over a single gait cycle at multiple right-side unilateral stiffness levels with a 90 kg subject. The origin of [0, 0] is the subject’s center of mass estimated by motion capture markers on the hips, projected on the walking plane. With this orientation of the figure, the subject is walking in the upward direction.